ADD AND SUBTRACT FRACTIONS WORKSHEET

1. Add 3/4  and 1/4.

2. Find the value of : 7/15 + 13/15 + 11/15.

3. Subtract 3/21 from 10/21.

4. Find the value of : 5/28 + 3/28 - 1/28.

5. Add 1/12 and 3/18.

6. Subtract 7/20 from 5/16.

7. Find the value of : 3/4 + 5/6 + 1/9.

8. Find the value of : 1/15 - 7/10 + 3/20.

9.  Naunet wants to fence off two side-by-side sections of her garden. Each section is 15/2 meters long and 2 meters wide. She says she needs 38 meters of fencing. Explain what is wrong with her thinking. How much fencing does she really need?

10.  What is the perimeter and area of the rectangle?.

11. Renee's desk has a rectangular top with a length of 3 1/4 feet and a width of 6 5/12 feet. What is the perimeter and area of the top of Renee's desk?

12. A square classroom has a perimeter of 30 yards. What is the length of each side of the classroom?

A) 15 yards     B) 20 yards    C) 3 3/4 yards

D) 7 1/2 yards

1. Answer :

3/4 + 1/4

The fractions above have the same denominator, that is 4.

So, take the denominator once and combine the numerators.

3/4 + 1/4 = (3 + 1)/4

= 4/4

= 1

2. Answer :

7/15 + 13/15 + 11/15

The fractions above have the same denominator, that is 15.

So, take the denominator once and simplify the numerators.

7/15 + 13/15 + 11/15 = (7 + 13 + 11)/15

= 31/15

3. Answer :

10/21 - 3/21

The fractions above have the same denominator, that is 21.

So, take the denominator once and simplify the numerators.

10/21 - 3/21 = (10 - 3)/21

= 7/21

= 1/3

4. Answer :

5/28 + 3/28 - 1/28

The fractions above have the same denominator, that is 28.

So, take the denominator once and simplify the numerators.

5/28 + 3/28 - 1/28 = (5 + 3 - 1)/28

= 7/28

= 1/4

5. Answer :

1/12 + 3/18

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (12, 18) = 36.

Now, make the denominator of each fraction 36 using multiplication.

1/12 = (1 ⋅ 3)/(12 ⋅ 3) = 3/36

3/18 = (3 ⋅ 2)/(18 ⋅ 2) = 6/36

1/12 + 3/18 :

= 3/36 + 6/36

= (3 + 6)/36

= 9/36

= 1/4

6. Answer :

5/16 - 7/20

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (16, 20) = 80.

Now, make the denominator of each fraction as 80 using multiplication.

5/16 = (5 ⋅ 5)/(16 ⋅ 5) = 25/80

7/20 = (7 ⋅ 4)/(20 ⋅ 4) = 28/80

5/16 - 7/20 :

= 25/80 - 28/80

= (25 - 28)/80

= -3/80

7. Answer :

3/4 + 5/6 + 1/9

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (4, 6, 9) = 36.

Now, make the denominator of each fraction as 36 using multiplication.

3/4 = (3 ⋅ 9)/(4 ⋅ 9) = 27/36

5/6 = (5 ⋅ 6)/(6 ⋅ 6) = 30/36

1/9 = (1 ⋅ 4)/(9 ⋅ 4) = 4/36

3/4 + 5/6 + 1/9 :

= 27/36 + 30/36 + 4/36

= (27 + 30 + 4)/36

= 61/36

8. Answer :

1/15 - 7/10 + 3/20

The fractions above have different denominators.

Find the least common multiple of the denominators.

Least common multiple of (15, 10, 20) = 60.

Now, make the denominator of each fraction as 60 using multiplication.

1/15 = (1 ⋅ 4)/(4 ⋅ 15) = 4/60

7/10 = (7 ⋅ 6)/(10 ⋅ 6) = 42/60

3/20 = (3 ⋅ 3)/(20 ⋅ 3) = 9/60

1/15 - 7/10 + 3/20 :

= 4/60 + 42/60 + 9/60

= (4 + 42 + 9)/60

= 55/60

= 11/12

9. Answer :

Perimeter of rectangular garden = 2(length + width)

Length = 15/2 meter and width = 2 meter

= 2(15/2 + 2)

= 2(15/2 + 2/1)

Making the denominators same, we get

= 2 (15 + 4)/2

= 2(19/2)

= 19 meter

So, perimeter of the rectangular garden is 19 meter. So, it is enough to have 19 meter length of fencing but she says 38 meters of fencing is needed. So, it is incorrect.

10. Answer :

From the rectangle above,

Length = 9  1/5 inches

Width = 1  3/10

Perimeter = 2(length + width)

= 2(9  1/5 + 1  3/10)

= 2(10 + 1/5 + 3/10)

= 2(10 + (2 + 3)/10))

= 2(10 + 5/10)

= 2(10 + 1/2)

= 2 (20 + 1)/2

= 2(21/2)

= 21 inches

Area of rectangle = length x width

= 9   1/5 x 1  3/10

Converting into mixed fraction, we get

= (46/5) x (13/10)

= 299/25

= 11   24/25 square inches.

11. Answer :

Lenght = 3  1/4 feet ==> 13/4

Width = 6  5/12 feet ==> 77/12

Perimeter of rectangle = 2(13/4 + 77/12)

= 2[(39 + 77) / 12]

= 2(116/12)

= 116/6

= 114  2/6 square feet

12. Answer :

Perimeter of square = 30 yards

4(side) = 30

Side = 30/4

= 15/2

Converting into mixed fraction, we get

= 7  1/2 yards.

So, option D is correct.

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